Question: The lifespans of lizards in a particular zoo are normally distributed. The average lizard lives $2.8$ years; the standard deviation is $0.3$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a lizard living between $2.2$ and $3.4$ years.
$2.8$ $2.5$ $3.1$ $2.2$ $3.4$ $1.9$ $3.7$ $95\%$ We know the lifespans are normally distributed with an average lifespan of $2.8$ years. We know the standard deviation is $0.3$ years, so one standard deviation below the mean is $2.5$ years and one standard deviation above the mean is $3.1$ years. Two standard deviations below the mean is $2.2$ years and two standard deviations above the mean is $3.4$ years. Three standard deviations below the mean is $1.9$ years and three standard deviations above the mean is $3.7$ years. We are interested in the probability of a lizard living between $2.2$ and $3.4$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $95\%$ of the lizards will have lifespans within 2 standard deviations of the average lifespan. The probability of a particular lizard living between $2.2$ and $3.4$ years is ${95\%}$.